AP Physics – Thermo – 3
1. A scuba tank has a volume of 1.50 L. The temperature is 25.0 °C. It is at a pressure of 315
atm. How many moles of air does the tank hold?
315 atm A 101.3 kPa/atm = 31,909.5 kPa
PV = nRT
n = PV/RT = 31,909.5 atm A 1.50 L/(8.31 kPaAL/molAK A 298 K) =
19.33 mol
2. What is the average velocity of the particles of hydrogen gas at 25.5 °C?
vrms =
=
=
1923.5 m/s
3. In a thermodynamic process, a system absorbs 755 kJ of heat and does 117 kJ of work on its
surroundings. By what amount did the system’s internal energy increase?
ÄU = Q + W
= 755 kJ + (!117) kJ
= 638 kJ
4. A steam engine operates on a warm 28.0 °C day. The saturated steam operates at a
temperature of 100.0 °C. What is the ideal efficiency for this engine?
ec =
= (373 K - 301 K)/373 K
= 0.193
5. 35.7 kJ of energy are required to raise the temperature of a gold statue from 25.0 °C to 435
°C. What is the mass of the gold?
Q = mcÄT
m = Q/cÄT = 35,700 J/(0.13 J/gK A 410 K) =
670. g
6. A 135.5 kg weight falls a distance of 12.5 m. It is attatched to a set of paddles that rotate in
an insulated tank of water. If the mass of the water is 3.5 kg and it begins at a temperature of
25.0°C, at what temperature does it end up?
Assuming 100% of the energy goes from the weight into the paddles, and 100%
of the energy from the paddles goes into heating the water...
Q = PE = mgh = 135.5 kg A 9.8 m/s2 A 12.5 m = 16,598.75 J
Q = mcÄT
ÄT= Q/mc = 16.6 kJ/(3.5 kg A 4.186 kJ/kgA°C) = 1.133 °C
Tf = Ti + ÄT = 25.0 °C + 1.1 °C =
26.1 °C
7. Three identical resistors, each of resistance 30 Ù are connected in a circuit to heat water in a
glass beaker. 24 V battery with negligible internal resistance provides the power.
a) The three resistors may be connected in series or in parallel.
i. If they are connected in series, what power is developed in the circuit?
ii. If they are connected in parallel, what power is developed in the circuit?
b) Using the battery
and one or more of
the resistors, design
a circuit that will
heat the water at the
fastest rate when the
resistor(s) are
placed in the water.
Include an ammeter
to measure the
current in the circuit
and a voltmeter to
measure the total
potential difference
of the circuit.
Assume the wires
are insulated and
have no resistance.
Draw a diagram of the circuit in the box, using the symbols shown to represent the
components in your diagram.
c) The resistor(s) in the circuit in part (b) are now immersed in a 0.5 kg sample of water,
which is initially at 298 K. The specific heat of water is 4,200 J/kg ·K. Assume that all
of the heat produced is absorbed by the water.
i. Calculate the amount of time it takes for the water to begin to boil.
ii. Under actual experimental conditions, would the time taken for the water to boil be
longer or shorter than the calculated time in part (c, i)? Justify your answer.
d) As the circuit continues to provide energy to the water, vapor is formed at the same
temperature as the boiling water. Where has the energy used to boil the water gone?
a) i. Rtotal = R1 + R2 + R3 = 30 Ù + 30 Ù + 30 Ù = 90 Ù
P = V2/R = 242 V2/90 Ù =
6.4 W
ii. Rtotal = (R1-1 + R2-1 + R3-1)-1 = 10 Ù
P = V2/R = 242 V2/10 Ù =
57.6 W
b)
c) i. Q = mcÄT
= 0.5 kg A (4200 J/kg AK) A 75 K = 157,500 J
t
= W/P = 157,500 J/57.6 W = 2734 s =
45 min 34 s
ii. Under experimental conditions, the time to boil the water should be
longer. We assume in our calculations that 100% of the heat goes into
the water (none into the resistor or the vessel the water is in), AND we
assume that the water doesn’t lose any of the heat it gained during the
45 minutes it’s building up the heat to reach boiling. In reality, some of
the heat would go into the other objects instead of the water, and the
water would lose heat over time, so more time would be required.
d) After the water has reached its boiling point, the extra energy goes into
allowing the water molecules to overcome their intermolecular attractions
and gain enough kinetic energy to “leap” up into the air and leave the liquid
behind.